he Koran explicitly forbids "riba," an Arabic word that Muslim jurists have defined as usury; it was banned to protect poorer classes from exploitative money lenders.

But many observant Muslims and experts in Shariah, or Islamic law, do not agree whether that prohibition bans any interest at all or only excessive interest.

"Shariah scholars have ruled both ways," said Timur Kuran, a professor of economics and the King Faisal professor of Islamic Thought and Culture at the University of Southern California in Los Angeles. "It's been a persistent controversy."

Because of that ambiguity, observant Muslims until fairly recently either financed their businesses and purchases in cash or agreed to pay and receive interest. Those who paid riba could invoke a necessity clause in the Koran; many who accepted it on savings would donate the interest earned to charity.

"It wasn't until the 1970's that this issue was even discussed, that there could be an Islamic, or interest-free, banking system," said Mahmoud A. El-Gamal, a professor of Islamic economics, finance and management at Rice University in Houston. Many Muslims were simply paying and collecting interest — "and not worrying about it," he added.

A growing number of Muslims, however, are seeking an alternative that adheres to the stricter interpretation of Islamic law.

"In the United States, there is a larger degree of conservatism among American Muslims, so there is more demand for Islamic banking," said Khaled Abou el Fadl, who teaches Islamic law at U.C.L.A.

One goal in Islamic finance is to have both partners — the bank and the buyer — share equally in the risk of a transaction. Because Islamic banks invest with their customers rather than lend to them, the risk of losing principal is greater and there is no fixed rate of return. In some cases, such transactions amount to nothing more exotic than the sort of lease that is familiar to many Western car buyers: the finance company buys a car and lets the customer drive it in exchange for monthly payments over a fixed period. When the term is up, the customer can buy the used car at the market price or enter another lease.

For homes, however, different approaches are used. To conform to Shariah, homebuyers and finance companies effectively become partners, either through lease-purchase agreements that resemble conventional financing or through self-help groups that pool money from Muslim investors to help one another buy houses.

Under lease-purchase programs, for example, a home buyer and the finance company pool their money to buy a house. The home owner agrees to make monthly payments that are split between repaying the company its capital and paying a fair-market rent on the property. The rent is split between the buyer and the financial institution according to how much each has invested in the house.

If, for example, the finance company put up 70 percent of the purchase price, it would receive 70 percent of the rent — that is the return on its investment. As the homebuyer repaid part of the capital each month, however, the institution's ownership stake in the house — and, therefore, its percentage of the rent — would decrease. Eventually, the homeowner would repay all the capital and the rent payments would cease.

At American Finance House-Lariba, an Islamic finance company in Pasadena, Calif., the lease-purchase program is similar in structure to a traditional mortgage so that a portion of each payment would qualify as tax deductible under the section of the tax code that covers interest payments. That allows Lariba to qualify for financing from Freddie Mac, the government-chartered private company that helps to finance home purchases.

Lariba is the first Islamic institution to receive Freddie Mac financing. It receives about 15 requests for loan applications every day, three times as many as last year, said M. Maguid Abdelaaty, the company's president.

"We're required to calculate the implied rate of return," he said, adding that the financing structure his company uses eases customers' mind about paying interest, "but the documentation, the note and the mortgage forms are the same" as for loans.